Steady ship motion in calm water is a classical problem in ship hydrodynamics. Potential flow modelling is a common method to predict the wave resistance of ships. In its conventional form the flow is assumed to be free from damping due to the inviscid assumption of potential flow. It has been argued by the founding fathers of ship resistance predictions that damping plays an important role in determining the wave resistance. Despite this viscosity is often omitted from present wave resistance prediction methods. It is known that damping plays an important role in the formation of the wave pattern and it is therefore of interest to determine the effect on the resistance prediction by including a damping factor in a previously undampened model. In this study, the problem is modelled using Kelvin sources with a translating speed. The fluid flow is modelled using a linearised free surface condition but an exact body condition on the hull. Rayleigh damping is introduced in the model to emulate viscous damping. To calculate the source influences, a new dissipative 3D Green function is derived. The image source part of Green function is separated into the near field and far field disturbance to achieve fast convergence of the integrals. The method is evaluated using thin ship theory to determine the wave pattern behind and the wave profile along a Wigley hull. A panel method is used to determine the wave and residual resistance for submerged ellipsoids and spheres. The results are validated and compared to existing numerical and experimental data from other sources. The results show that it may be possible to capture the residual resistance by including damping in a potential flow model but that more evaluations are needed.